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The electronic structure of the toroid D$_{6h}$-Au$_{42}$ is studied withinthe framework of the Hubbard Hamiltonian in the approximation of staticfluctuations. An expression for the Fourier transform of the Green's function,the poles of which determine the energy spectrum of the nanocluster underconsideration, is obtained. The energy spectrum of the D$_{6h}$-Au$_{42}$toroid indicates that the nanosystem is in a metallic state. Graphicalrepresentations of the equation for the chemical potential and the density ofstate of electrons are presented. The spectrum of optical absorption is shown,the energies of direct optical transitions D$_{6h}$-Au$_{42}$ are 0.95 eV, 1.24eV, 1.39 eV, are in the near infrared region. The energy of the ground state iscalculated for the electrically neutral as well as for the positively andnegatively charged ions of the toroid. The possibility of using of theinvestigated toroid from Au atoms for the diagnostics and treatment of canceris shown.

Study of the electronic structure and optical absorption spectrum of the gold aromatic toroid D$_{6h}$-Au$_{42}$